Questions: Calculate the future value of 9,000 earning 5% interest compounded quarterly for 7 years. (Round your answer to the nearest cent.) Enter a number.

Solution Steps

To convert the annual interest rate to a decimal, divide the rate by 100: $r\% \rightarrow \frac{r}{100} = \frac{5}{100} = 0.05$.

The rate per period is calculated as $\frac{r}{n} = \frac{0.05}{4} = 0.0125$.

The growth factor per period is $1 + \frac{r}{n} = 1 + 0.0125 = 1.012$.

The total number of compounding periods is $n \times t = 4 \times 7 = 28$.

The compound growth factor is $(1 + \frac{r}{n})^{nt} = 1.012^{28} = 1.416$.

The future value is $P \times (1 + \frac{r}{n})^{nt} = 9000 \times 1.416 = 12743.93$.

Final Answer: The future value of the investment is $12743.93.